sumPvalsPar: True Discovery Guarantee for p-Value Combinations -...

In annavesely/sumSome: True Discovery Guarantee by Sum-Based Tests

True Discovery Guarantee for p-Value Combinations - Parametric

Description

This function uses p-values to determine confidence bounds for the number of true discoveries, the true discovery proportion and the false discovery proportion within a set of interest. The bounds are simultaneous over all sets, and remain valid under post-hoc selection.

Usage

sumPvalsPar(g, S = NULL, alpha = 0.05, type = "vovk.wang", r = 0, independence = NULL)

Arguments

g	numeric vector of p-values.
S	vector of indices for the variables of interest (if not specified, all variables).
alpha	significance level.
type	p-value combination among fisher, pearson, liptak, cauchy, harmonic, vovk.wang (see details).
r	parameter for Vovk and Wang's p-value combination.
independence	logical, TRUE to assume independence, FALSE for general dependence structure. If not specified, it is set to FALSE for vovk.wang, and TRUE otherwise.

Details

A p-value p is transformed as following.

• Fisher: -2log(p) (Fisher, 1925)

• Pearson: 2log(1-p) (Pearson, 1933)

• Liptak: qnorm(1-p) (Liptak, 1958; Stouffer et al., 1949)

• Cauchy: tan[(0.5-p)pi] with pi=3.142 (Liu and Xie, 2020)

• Harmonic mean: 1/p (Wilson, 2019)

• Vovk and Wang: p^r (log(p) for r=0) (Vovk and Wang, 2020)

An error message is returned if the transformation produces infinite values.

For Vovk and Wang, r=-Inf corresponds to the minimum p-value, r=Inf to the maximum p-value, r=0 to Fisher, and r=-1 to the harmonic mean.

Under independence, for Vovk and Wang the test is defined only for r=0 and r=1. Under general dependence, the test is defined only for Fisher, the harmonic mean and Vovk and Wang.

For combinations that are not implemented, if the vector of critical values is known the method can be applied through sumStatsPar. Please contact us to implement other known vectors of critical values that do not currently appear.

Value

sumPvalsPar returns an object of class sumObj, containing

• total: total number of variables (length of g)

• size: size of S

• alpha: significance level

• TD: lower (1-alpha)-confidence bound for the number of true discoveries in S

• maxTD: maximum value of TD that could be found under convergence of the algorithm

• iterations: number of iterations of the algorithm (NULL)

Author(s)

Xu Chen.

References

Goeman J. J. and Solari A. (2011). Multiple testing for exploratory research. Statistical Science, doi: 10.1214/11-STS356.

Tian J., Chen X., Katsevich E., Goeman J. J. and Ramdas A. (2022). Large-scale simultaneous inference under dependence. Scandinavian Journal of Statistics, doi: 10.1111/sjos.12614.

See Also

True discovery guarantee using generic statistics (parametric): sumStatsPar

Access a sumObj object: discoveries, tdp, fdp

Examples

# generate vector of p-values for 5 variables
g <- as.vector(simData(prop = 0.6, m = 5, B = 1, alpha = 0.4, seed = 42))

# subset of interest (variables 1 and 2)
S <- c(1,2)
 
# create object of class sumObj
# combination: harmonic mean under general dependence
res <- sumPvalsPar(g, S, alpha = 0.4, type = "harmonic", independence = FALSE)
res
summary(res)

# lower confidence bound for the number of true discoveries in S
discoveries(res)

# lower confidence bound for the true discovery proportion in S
tdp(res)

# upper confidence bound for the false discovery proportion in S
fdp(res)

annavesely/sumSome documentation built on Jan. 28, 2025, 8:15 a.m.